Inequalities for the Norm and Numerical Radius of Composite Operators in Hilbert Spaces

Some new inequalities for the norm and the numerical radius of composite operators generated by a pair of operators are given.Comment: 12 page

Reverses of the Triangle Inequality in Banach Spaces

Recent reverses for the discrete generalised triangle inequality and its continuous version for vector-valued integrals in Banach spaces are surveyed. New results are also obtained. Particular instances of interest in Hilbert spaces and for complex numbers and functions are pointed out as well.Comment: 48 page

Gruss Type Discrete Inequalities in Normed Linear Spaces, Revisited

Some sharp inequalities of Gruss type for sequences of vectors in real or complex normed linear spaces are obtained. Applications for the discrete Fourier and Mellin transform are given. Estimates for polynomials with coefficients in normed spaces are provided as well

On Pecaric's Inequality in Inner Product Spaces

Some related results to Pecaric's inequality in inner product spaces that generalises Bombieri's inequality, are given

New Reverses of Schwarz, Triangle and Bessel Inequalities in Inner Product Spaces

New reverses of the Schwarz, triangle and Bessel inequalities in inner product spaces are pointed out. These results complement the recent ones obtained by the author in an earlier paper. Further, they are employed to establish new Gruss type inequalities. Finally, some natural integral inequalities are stated as well

Some Trace Inequalities for Operators in Hilbert Spaces

Some new trace inequalities for operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated and applications for power series of such operators are given. Some trace inequalities for matrices are also derived. Examples for the operator exponential and other similar functions are presented as well